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arXiv:1410.4293 · Applied Physics Letters

Observation of the fundamental Nyquist noise limit in an ultra-high Q-factor cryogenic bulk acoustic wave cavity

Maxim Goryachev, Eugene N. Ivanov, Frank J. van Kann, Serge Galliou, Michael Edmund Tobar

Published Oct 13, 2014• 33 citations

Abstract

Thermal Nyquist noise fluctuations of high-Q bulk acoustic wave cavities have been observed at cryogenic temperatures with a DC superconducting quantum interference device amplifier. High Q modes with bandwidths of few tens of milliHz produce thermal fluctuations with a signal-to-noise ratio of up to 23 dB. The estimated effective temperature from the Nyquist noise is in good agreement with the physical temperature of the device, confirming the validity of the equivalent circuit model and the non-existence of any excess resonator self-noise. The measurements also confirm that the quality factor remains extremely high (Q > 108 at low order overtones) for very weak (thermal) system motion at low temperatures, when compared to values measured with relatively strong external excitation. This result represents an enabling step towards operating such a high-Q acoustic device at the standard quantum limit.

DOI: 10.1063/1.4898813

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Thermal Nyquist noise fluctuations of high-Q bulk acoustic wave cavities have been observed at cryogenic temperatures with a DC superconducting quantum interference device amplifier. High Q modes with bandwidths of few tens of milliHz produce thermal fluctuations with a signal-to-noise ratio of up to 23 dB. The estimated effective temperature from the Nyquist noise is in good agreement with the physical temperature of the device, confirming the validity of the equivalent circuit model and the non-existence of any excess resonator self-noise. The measurements also confirm that the quality factor remains extremely high (Q > 108 at low order overtones) for very weak (thermal) system motion at low temperatures, when compared to values measured with relatively strong external excitation. This result represents an enabling step towards operating such a high-Q acoustic device at the standard quantum limit.

A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10¹⁸ Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID) amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structure of the spectrum in both incident power and frequency. The result gives an insight into the open loop behaviour of a future Cryogenic Quartz Oscillator in the strong signal regime.

A dc superconducting quantum interference device (SQUID) with a resonant microstrip input and a cooled heterostructure field-effect transistor as a postamplifier is used as a radio-frequency amplifier in the frequency range 90–500 MHz. At liquid He3 temperatures, gains of 24 and 20 dB and intrinsic noise temperatures of 0.06±0.02 and 0.12±0.10 K were achieved at 89.6 and 438 MHz, respectively. The system noise temperature at 438 MHz was also estimated from the Nyquist noise produced by a resonant circuit coupled to the input of the microstrip SQUID.

We demonstrate that Bulk Acoustic Wave (BAW) quartz resonator cooled down to millikelvin temperatures are excellent building blocks for hybrid quantum systems with extremely long coherence times. Two overtones of the longitudinal mode at frequencies of 15.6 and 65.4 MHz demonstrate a maximum f.Q product of 7.8×1016 Hz. With this result, the Q-factor in such devices near the quantum ground state can be four orders of magnitude better than previously attained in other mechanical systems. Tested quartz resonators possess the ultra low acoustic losses crucial for electromagnetic cooling to the phonon ground state.

We present measurements of an amplifier operating at 3.8 GHz with 150 MHz of bandwidth based on the microstrip input-coil resonance of a dc superconducting quantum interference device (SQUID) with submicron Josephson junctions. The noise temperature is measured using two methods: comparing the signal-to-noise ratio of the system with and without the SQUID in the amplifier chain, and using a modified Y-factor technique where calibrated narrowband noise is mixed up to the SQUID amplifier operating frequency. With the SQUID cooled to 0.35 K, we observe a minimum system noise temperature of 0.55 ± 0.13 K, dominated by the contribution from the SQUID amplifier.

A dc superconducting quantum interference device (SQUID) with a resonant microstrip input is operated as an amplifier at temperatures down to 20 mK. A second SQUID is used as a postamplifier. Below about 100 mK, the noise temperature is 52±20 mK at 538 MHz, estimated from measurements of signal-to-noise ratio, and 47±10 mK at 519 MHz, estimated from the noise generated by a resonant circuit coupled to the input. The quantum-limited noise temperatures are 26 and 25 mK, respectively. The measured noise temperature is limited by hot electrons generated by the bias current.